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Ordinal classification problems, where labels exhibit a natural order, are prevalent in high-stakes fields such as medicine and finance. Accurate uncertainty quantification, including the decomposition into aleatoric (inherent variability)…

Machine Learning · Computer Science 2025-07-02 Stefan Haas , Eyke Hüllermeier

Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…

Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…

Atmospheric and Oceanic Physics · Physics 2025-12-01 Laura A. Mansfield , Hannah M. Christensen

The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…

Machine Learning · Computer Science 2025-08-19 Freddie Bickford Smith , Jannik Kossen , Eleanor Trollope , Mark van der Wilk , Adam Foster , Tom Rainforth

We provide single-model estimates of aleatoric and epistemic uncertainty for deep neural networks. To estimate aleatoric uncertainty, we propose Simultaneous Quantile Regression (SQR), a loss function to learn all the conditional quantiles…

Machine Learning · Statistics 2019-09-09 Natasa Tagasovska , David Lopez-Paz

Concept Bottleneck Models (CBMs) predict through human-interpretable concepts, but they typically output point concept probabilities that conflate epistemic uncertainty (reducible model underspecification) with aleatoric uncertainty…

Artificial Intelligence · Computer Science 2026-04-28 Tanmoy Mukherjee , Thomas Bailleux , Pierre Marquis , Zied Bouraoui

Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever…

We present a novel approach to uncertainty quantification in classification tasks based on label-wise decomposition of uncertainty measures. This label-wise perspective allows uncertainty to be quantified at the individual class level,…

Machine Learning · Computer Science 2024-06-05 Yusuf Sale , Paul Hofman , Timo Löhr , Lisa Wimmer , Thomas Nagler , Eyke Hüllermeier

Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…

Machine Learning · Computer Science 2023-10-26 Tsai Hor Chan , Kin Wai Lau , Jiajun Shen , Guosheng Yin , Lequan Yu

Aleatoric and Epistemic uncertainty have achieved recent attention in the literature as different sources from which uncertainty can emerge in stochastic modeling. Epistemic being intrinsic or model based notions of uncertainty, and…

Methodology · Statistics 2025-08-15 Ryan Warnick

Brain vessel segmentation of MR scans is a critical step in the diagnosis of cerebrovascular diseases. Due to the fine vessel structure, manual vessel segmentation is time consuming. Therefore, automatic deep learning (DL) based…

Image and Video Processing · Electrical Eng. & Systems 2025-03-31 Omini Rathore , Richard Paul , Abigail Morrison , Hanno Scharr , Elisabeth Pfaehler

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…

Machine Learning · Computer Science 2024-04-22 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

Deep learning has emerged as a promising paradigm to give access to highly accurate predictions of molecular and materials properties. A common short-coming shared by current approaches, however, is that neural networks only give point…

Computational Physics · Physics 2023-05-10 Albert Zhu , Simon Batzner , Albert Musaelian , Boris Kozinsky

In a data-scarce field such as healthcare, where models often deliver predictions on patients with rare conditions, the ability to measure the uncertainty of a model's prediction could potentially lead to improved effectiveness of decision…

Machine Learning · Statistics 2020-05-26 Lotta Meijerink , Giovanni Cinà , Michele Tonutti

Datasets collected from the open world unavoidably suffer from various forms of randomness or noiseness, leading to the ubiquity of aleatoric (data) uncertainty. Quantifying such uncertainty is particularly pivotal for object detection,…

Computer Vision and Pattern Recognition · Computer Science 2024-11-28 Peng Cui , Guande He , Dan Zhang , Zhijie Deng , Yinpeng Dong , Jun Zhu

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…

Machine Learning · Statistics 2025-09-11 Marzieh Ajirak , Anand Ravishankar , Petar M. Djuric

Uncertainty estimation bears the potential to make deep learning (DL) systems more reliable. Standard techniques for uncertainty estimation, however, come along with specific combinations of strengths and weaknesses, e.g., with respect to…

Machine Learning · Computer Science 2022-05-02 Joachim Sicking , Maram Akila , Jan David Schneider , Fabian Hüger , Peter Schlicht , Tim Wirtz , Stefan Wrobel

Identifying and disentangling sources of predictive uncertainty is essential for trustworthy supervised learning. We argue that widely used second-order methods that disentangle aleatoric and epistemic uncertainty are fundamentally…

Machine Learning · Computer Science 2026-02-09 Sebastián Jiménez , Mira Jürgens , Willem Waegeman

Uncertainty estimation is an essential step in the evaluation of the robustness for deep learning models in computer vision, especially when applied in risk-sensitive areas. However, most state-of-the-art deep learning models either fail to…

Computer Vision and Pattern Recognition · Computer Science 2022-01-12 Lu Mi , Hao Wang , Yonglong Tian , Hao He , Nir Shavit

Assessing the quality of aleatoric uncertainty estimates from uncertainty quantification (UQ) deep learning methods is important in scientific contexts, where uncertainty is physically meaningful and important to characterize and interpret…

Machine Learning · Computer Science 2024-11-14 Rebecca Nevin , Aleksandra Ćiprijanović , Brian D. Nord